Hurst Parameter as a Correlation Measure for Brain Signal

Abstract:The frequency of ventricular premature beats (VPBs) has been related to the risk of mortality. However, little is known about the temporal pattern of occurrence of VPBs and its relationship to autonomic activity. Hence, we applied a general correlation measure, mutual information, to quantify how VPBs are generated over time. We also used mutual information to determine the correlation between VPB production and heart rate in order to evaluate effects of autonomic activity on VPB production. We examined twenty subjects with more than 3000 VPBs/day and simulated ran-( dom time series of VPB occurrence. We found that mutual information values could be used to characterize quantitatively the temporal patterns of VPB generation. Our data suggest that VPB production is not random and VPBs generated with a higher value of mutual information may be more greatly affected by autonomic activity.

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Correlation Measure for Big Data

Journal of Applied Reliability ◽

10.33162/jar.2018.09.18.3.208 ◽

2018 ◽

Vol 18 (3) ◽

pp. 208-212

Author(s):

Hai Sung Jeong

Keyword(s):

Big Data ◽

Correlation Measure

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Global attracting sets of neutral stochastic functional integro-differential equations driven by a fractional Brownian motion

Random Operators and Stochastic Equations ◽

10.1515/rose-2021-2058 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

A. Bakka ◽

S. Hajji ◽

D. Kiouach

Keyword(s):

Hilbert Space ◽

Fixed Point ◽

Brownian Motion ◽

Differential Equations ◽

Fractional Brownian Motion ◽

Sufficient Conditions ◽

Integrodifferential Equations ◽

Hurst Parameter ◽

Fixed Point Principle ◽

Stochastic Functional

Abstract By means of the Banach fixed point principle, we establish some sufficient conditions ensuring the existence of the global attracting sets of neutral stochastic functional integrodifferential equations with finite delay driven by a fractional Brownian motion (fBm) with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} in a Hilbert space.

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Malliavin calculus used to derive a stochastic maximum principle for system driven by fractional Brownian and standard Wiener motions with application

Random Operators and Stochastic Equations ◽

10.1515/rose-2020-2047 ◽

2020 ◽

Vol 28 (4) ◽

pp. 291-306

Author(s):

Tayeb Bouaziz ◽

Adel Chala

Keyword(s):

Brownian Motion ◽

Maximum Principle ◽

Control Problem ◽

Fractional Brownian Motion ◽

Stochastic Control ◽

Malliavin Calculus ◽

Stochastic Maximum Principle ◽

Hurst Parameter ◽

Principle Of Optimality ◽

Initial Cost

AbstractWe consider a stochastic control problem in the case where the set of the control domain is convex, and the system is governed by fractional Brownian motion with Hurst parameter {H\in(\frac{1}{2},1)} and standard Wiener motion. The criterion to be minimized is in the general form, with initial cost. We derive a stochastic maximum principle of optimality by using two famous approaches. The first one is the Doss–Sussmann transformation and the second one is the Malliavin derivative.

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